please do all the questions!

9. A proposition that can be proven to be true within an axtom syatem is: (a) an axiokn (b) a theorem (c) a definition (d) a paradox 10. P(x)=x2>0 is (a) true (b) false (c) a boolean variable (d) a propositional function 11. Which of the following statementa is FALSE? (a) Not all infinite sets have the same cardindlity (b) If A is countable then AA is countable (c) {{}} (d) Proofs by induction can be used only on countsble sots 12. The inductive bypotbesis of every inductive proof mugt include the statement "for a fixed (arbitrary) k ", othervise (a) n would not be even (b) we would not be able to compute k+1 (c) We would obtain Russell's paradox (d) We would assume what we want to prove